Master IP Subnetting: From Binary Conversion to CIDR Calculations

Fundamental Concepts

Subnet : Division of a larger network into equal‑size smaller networks.

Binary‑to‑decimal conversion for IP calculations : Count the number of "1" bits and use 2^n for each position rather than summing low‑order powers.

Number of networks : A‑class 2^7 − 2 usable, B‑class 2^14 − 2 usable, C‑class 2^21 − 2 usable.

Total IPs per class : A = 2^24, B = 2^16, C = 2^8; usable = total − 2.

Mask purpose : Indicates how many subnets a large network is split into; the mask’s 1‑bits define the network portion.

Decimal‑to‑8‑bit binary table (0‑255): 128 = 10000000, 64 = 01000000, …, 1 = 00000001.

Default Masks

A‑class: 255.0.0.0 (11111111.00000000.00000000.00000000)

B‑class: 255.255.0.0 (11111111.11111111.00000000.00000000)

C‑class: 255.255.255.0 (11111111.11111111.11111111.00000000)

Valid Mask Rules

A mask is valid if, after conversion to binary, all leading bits are 1 and no 0 appears between 1s. Example: 255.255.248.0 → 11111111.11111111.11111000.00000000 (valid); 254.255.248.0 → 11111110… (invalid).

CIDR Notation

Mask 255.255.248.0 equals /21 because it contains 21 leading 1s. Conversely, /21 expands to the dotted‑decimal mask.

Unusable Addresses

Each network (including subnets) has two unusable addresses: the network address and the broadcast address.

Determining Subnet Count from a Mask

Identify the default‑mask class the given mask falls under, then count the extra leading 1s beyond the default. Example: 202.117.12.36/30 → mask 255.255.255.252 (binary 11111111.11111111.11111111.11111100) is within the C‑class range, giving 6 extra 1s → 2⁶ = 64 subnets, each with 4 IPs (2 usable).

Comprehensive Example

Given IP 172.31.128.255/18:

Subnet count: /18 adds two 1s to the B‑class default (/16), so 2² = 4 subnets.

Network address: IP AND mask → 172.31.128.0.

Host portion: IP AND inverse mask → 0.0.0.255 (host number 255).

Broadcast address: set host bits to 1 → 172.31.191.255.

Usable IP range: 172.31.128.1 – 172.31.191.254.

These steps illustrate binary‑decimal conversion, mask application, and derivation of network details for any subnetting problem.